What we discovered is the best way to see the botanical gardens is start right off of this lane and grab the tram.  It snakes through the left side of the map (north end) past a lot of the forests and tree collections--things that are good to see from a tram.  Then jump off the tram at the back of the park and walk your way back to the front on the right side of the map seeing most of the exhibits.

The botanical garden also has a nice restaurant/cafe for snacks or a whole meal or even just grabbing something to drink.